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In Afghanistan the literacy rate is 28.1%. For a random sample of 15 people, X ~ B(15, 0.281). What are the mean and standard deviation of the number of literate people in the sample?
Aμ ≈ 4.22, σ ≈ 2.81
Bμ ≈ 4.22, σ ≈ 1.74
Cμ ≈ 2.81, σ ≈ 1.74
Dμ ≈ 15.0, σ ≈ 0.28
Answer & Solution
Correct answer: B. μ ≈ 4.22, σ ≈ 1.74
1. μ = np = (15)(0.281) = 4.215, which rounds to about 4.22.
2. σ = sqrt(npq) = sqrt((15)(0.281)(0.719)) ≈ 1.7409, which rounds to about 1.74.
3. So on average about 4.22 people in the sample are literate, with a spread of roughly 1.74 people.
4. Option A swaps σ for p, and option C halves the mean, so neither matches the formulas.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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